test2_sol - EML 4312 Fall 2007 Root Locus, Continued...

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EML 4312 Fall 2007 Root Locus, Continued Fraction Expansion, MC/AC, Graphical Methods The due date for this assignment is Friday 10/12. For all the problems assume a cannonical feedback loop with a proportional controller. 1. (25 total points) Draw the root locus for the following open-loop transfer functions (you do not have to compute breakaway points). (a) (15 points) H ( s )= ( s +2)( s +1) ( s 1) 2 ( s +5)( s +5+ j )( s +5 j ) -20 -15 -10 -5 0 5 -15 -10 -5 0 5 10 15 Root Locus Real Axis Imaginary Axis If you missed this problem bring your test to class on Monday Nov. 5th. (b) (5 points) H ( s )= 1 ( s +1)( s +2)( s +3) -8 -7 -6 -5 -4 -3 -2 -1 0 1 -5 -4 -3 -2 -1 0 1 2 3 4 5 Root Locus Imaginary Axis
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(c) (5 points) H ( s )= 2 ( s +2)( s +4) -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 Root Locus Real Axis Imaginary Axis 2. (25 points) Use coe cient matching AND verify your answer with the graph- ical method to f nd a value of k that gives a closed-loop pole location of
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test2_sol - EML 4312 Fall 2007 Root Locus, Continued...

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